The slow-scale stochastic simulation algorithm (ssSSA) proposed in [J. Chem. Phys. 122, 014116 (2005)] and the nested stochastic simulation algorithm (nSSA) proposed in [J. Chem. Phys. 123,194107 (2005)] are closely related approximate simulation procedures aimed at speeding up the stochastic simulation of stiff chemical systems, i.e., systems that evolve through fast and slow dynamical modes w...

We present a study of the spatial correlation functions of a one-dimensional reaction-diffusion system in both equilibrium and out of equilibrium. For the numerical simulations we have employed the Gillespie algorithm dividing the system into cells to treat diffusion as a chemical process between adjacent cells. We find that the spatial correlations are spatially short ranged in equilibrium but...

The Gillespie Stochastic Simulation Algorithm (GSSA) and its variants are cornerstone techniques to simulate reaction kinetics in situations where the concentration of the reactant is too low to allow deterministic techniques such as differential equations. The inherent limitations of the GSSA include the time required for executing a single run and the need for multiple runs for parameter swee...

Stochastic simulation has been widely used to model the dynamics of biochemical reaction networks. Several algorithms have been proposed that are exact solutions of the chemical master equation, following the work of Gillespie. These stochastic simulation approaches can be broadly classified into two categories: network-based and -free simulation. The network-based approach requires that the fu...

How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast–slow systems is investigated. In particular, it is shown via analysis of central limit theorem (CLT) and large deviation principle (LDP) that the standard version of HMM artificially amplifies these fluctuations. A simple modification of HMM, termed parallel HMM, is introduced and is shown to rem...

Pedersen and Sherman have recently developed a multi-pool model of insulin vesicle secretion from pancreatic beta-cells [12]. In the PedersenSherman model, pool sizes are reported as concentrations; however, concentrations of the different pools vary by as much as seven orders of magnitude. Very low concentrations indicate there could be discrete numbers of vesicles in some of the pools, leadin...

This study considers using Metropolis-Hastings algorithm for stochastic simulation of chemical reactions. The proposed method uses SSA (Stochastic Simulation Algorithm) distribution which is a standard method for solving well-stirred chemically reacting systems as a desired distribution. A new numerical solvers based on exponential form of exact and approximate solutions of CME (Chemical Master...

In this paper, we revisit the Nested Stochastic Simulation Algorithm (NSSA) for stochastic chemical reacting networks by first proving its strong convergence. We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes, for which strong error estimates can also be obtained. Numerical experiments are p...

We examine, in a discrete-stochastic setting, the benefits and liabilities of replacing the three-reaction set 1 2 3 S S S → ⇌ with a single 3 S -producing reaction. We develop a novel criterion for deciding whether such an abridgment can be accomplished in a way that accurately replicates the production of 3 S molecules, and we derive a formula for estimating the consequent speedup in stochast...